Problem: $h(t) = 7t+1$ $f(x) = 5x^{2}-5(h(x))$ $g(t) = -2t^{3}+5t^{2}-5(h(t))$ $ f(h(0)) = {?} $
Solution: First, let's solve for the value of the inner function, $h(0)$ . Then we'll know what to plug into the outer function. $h(0) = (7)(0)+1$ $h(0) = 1$ Now we know that $h(0) = 1$ . Let's solve for $f(h(0))$ , which is $f(1)$ $f(1) = 5(1^{2})-5(h(1))$ To solve for the value of $f$ , we need to solve for the value of $h(1)$ $h(1) = (7)(1)+1$ $h(1) = 8$ That means $f(1) = 5(1^{2})+(-5)(8)$ $f(1) = -35$